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  • \$\begingroup\$ I think there's a simpler argument -- the only places the matching can violate the sorted order is when two things cross like C->Y, D->X, and those can just be uncrossed. \$\endgroup\$ Commented Jan 25, 2016 at 5:18
  • \$\begingroup\$ @xnor That's basically what I wrote. Just with a lot more words. :P \$\endgroup\$ Commented Jan 25, 2016 at 5:21